Answer
$x=\left\{ -\dfrac{5}{2},3 \right\}$
Work Step by Step
The two numbers whose product is $ac=
2(-15)=-30
$ and whose sum is $b=
-1
$ are $\{
-6,5
\}$. Using these two numbers to decompose the middle term of the given equation, $
2x^2-x-15=0
,$ results to
\begin{array}{l}\require{cancel}
2x^2-6x+5x-15=0
\\\\
(2x^2-6x)+(5x-15)=0
\\\\
2x(x-3)+5(x-3)=0
\\\\
(x-3)(2x+5)=0
.\end{array}
Equating each factor to zero (or the Zero-Factor Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
x-3=0
\\\\
x=3
,\\\\\text{OR}\\\\
2x+5=0
\\\\
2x=-5
\\\\
x=-\dfrac{5}{2}
.\end{array}
Hence, the solutions are $
x=\left\{ -\dfrac{5}{2},3 \right\}
.$